LMFDB - Embedded newform 546.8.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,8,Mod(1,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	546.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$170.562223914$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 19438x^{2} + 79570x + 87003600 $ x^4 - x^3 - 19438x^2 + 79570x + 87003600
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$93.9054$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -301.420 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -301.420 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +2411.36 q^{10} -2295.22 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +8138.34 q^{15} +4096.00 q^{16} -2505.49 q^{17} -5832.00 q^{18} -4171.46 q^{19} -19290.9 q^{20} -9261.00 q^{21} +18361.7 q^{22} +30284.2 q^{23} +13824.0 q^{24} +12729.0 q^{25} +17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +129054. q^{29} -65106.7 q^{30} -193346. q^{31} -32768.0 q^{32} +61970.9 q^{33} +20044.0 q^{34} -103387. q^{35} +46656.0 q^{36} -129293. q^{37} +33371.7 q^{38} +59319.0 q^{39} +154327. q^{40} -310763. q^{41} +74088.0 q^{42} +240878. q^{43} -146894. q^{44} -219735. q^{45} -242273. q^{46} +575985. q^{47} -110592. q^{48} +117649. q^{49} -101832. q^{50} +67648.4 q^{51} -140608. q^{52} +150363. q^{53} +157464. q^{54} +691824. q^{55} -175616. q^{56} +112630. q^{57} -1.03243e6 q^{58} +2.69804e6 q^{59} +520854. q^{60} -804145. q^{61} +1.54677e6 q^{62} +250047. q^{63} +262144. q^{64} +662220. q^{65} -495767. q^{66} -3.80152e6 q^{67} -160352. q^{68} -817673. q^{69} +827097. q^{70} +3.76508e6 q^{71} -373248. q^{72} +5.02926e6 q^{73} +1.03434e6 q^{74} -343684. q^{75} -266974. q^{76} -787259. q^{77} -474552. q^{78} -6.27040e6 q^{79} -1.23462e6 q^{80} +531441. q^{81} +2.48610e6 q^{82} +3.15204e6 q^{83} -592704. q^{84} +755206. q^{85} -1.92702e6 q^{86} -3.48447e6 q^{87} +1.17515e6 q^{88} +1.23808e7 q^{89} +1.75788e6 q^{90} -753571. q^{91} +1.93819e6 q^{92} +5.22034e6 q^{93} -4.60788e6 q^{94} +1.25736e6 q^{95} +884736. q^{96} +4.74801e6 q^{97} -941192. q^{98} -1.67321e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} - 108 q^{3} + 256 q^{4} - 134 q^{5} + 864 q^{6} + 1372 q^{7} - 2048 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q - 32 * q^2 - 108 * q^3 + 256 * q^4 - 134 * q^5 + 864 * q^6 + 1372 * q^7 - 2048 * q^8 + 2916 * q^9	\( 4 q - 32 q^{2} - 108 q^{3} + 256 q^{4} - 134 q^{5} + 864 q^{6} + 1372 q^{7} - 2048 q^{8} + 2916 q^{9} + 1072 q^{10} - 5443 q^{11} - 6912 q^{12} - 8788 q^{13} - 10976 q^{14} + 3618 q^{15} + 16384 q^{16} + 45437 q^{17} - 23328 q^{18} - 11194 q^{19} - 8576 q^{20} - 37044 q^{21} + 43544 q^{22} + 17762 q^{23} + 55296 q^{24} + 64926 q^{25} + 70304 q^{26} - 78732 q^{27} + 87808 q^{28} - 24980 q^{29} - 28944 q^{30} - 15419 q^{31} - 131072 q^{32} + 146961 q^{33} - 363496 q^{34} - 45962 q^{35} + 186624 q^{36} - 602081 q^{37} + 89552 q^{38} + 237276 q^{39} + 68608 q^{40} - 596814 q^{41} + 296352 q^{42} - 697726 q^{43} - 348352 q^{44} - 97686 q^{45} - 142096 q^{46} - 238097 q^{47} - 442368 q^{48} + 470596 q^{49} - 519408 q^{50} - 1226799 q^{51} - 562432 q^{52} + 752377 q^{53} + 629856 q^{54} - 2846467 q^{55} - 702464 q^{56} + 302238 q^{57} + 199840 q^{58} + 1651268 q^{59} + 231552 q^{60} + 178667 q^{61} + 123352 q^{62} + 1000188 q^{63} + 1048576 q^{64} + 294398 q^{65} - 1175688 q^{66} + 658872 q^{67} + 2907968 q^{68} - 479574 q^{69} + 367696 q^{70} + 191640 q^{71} - 1492992 q^{72} + 49572 q^{73} + 4816648 q^{74} - 1753002 q^{75} - 716416 q^{76} - 1866949 q^{77} - 1898208 q^{78} + 131485 q^{79} - 548864 q^{80} + 2125764 q^{81} + 4774512 q^{82} + 20201469 q^{83} - 2370816 q^{84} + 10179117 q^{85} + 5581808 q^{86} + 674460 q^{87} + 2786816 q^{88} + 13736753 q^{89} + 781488 q^{90} - 3014284 q^{91} + 1136768 q^{92} + 416313 q^{93} + 1904776 q^{94} + 21017342 q^{95} + 3538944 q^{96} + 572361 q^{97} - 3764768 q^{98} - 3967947 q^{99}+O(q^{100}) \) 4 * q - 32 * q^2 - 108 * q^3 + 256 * q^4 - 134 * q^5 + 864 * q^6 + 1372 * q^7 - 2048 * q^8 + 2916 * q^9 + 1072 * q^10 - 5443 * q^11 - 6912 * q^12 - 8788 * q^13 - 10976 * q^14 + 3618 * q^15 + 16384 * q^16 + 45437 * q^17 - 23328 * q^18 - 11194 * q^19 - 8576 * q^20 - 37044 * q^21 + 43544 * q^22 + 17762 * q^23 + 55296 * q^24 + 64926 * q^25 + 70304 * q^26 - 78732 * q^27 + 87808 * q^28 - 24980 * q^29 - 28944 * q^30 - 15419 * q^31 - 131072 * q^32 + 146961 * q^33 - 363496 * q^34 - 45962 * q^35 + 186624 * q^36 - 602081 * q^37 + 89552 * q^38 + 237276 * q^39 + 68608 * q^40 - 596814 * q^41 + 296352 * q^42 - 697726 * q^43 - 348352 * q^44 - 97686 * q^45 - 142096 * q^46 - 238097 * q^47 - 442368 * q^48 + 470596 * q^49 - 519408 * q^50 - 1226799 * q^51 - 562432 * q^52 + 752377 * q^53 + 629856 * q^54 - 2846467 * q^55 - 702464 * q^56 + 302238 * q^57 + 199840 * q^58 + 1651268 * q^59 + 231552 * q^60 + 178667 * q^61 + 123352 * q^62 + 1000188 * q^63 + 1048576 * q^64 + 294398 * q^65 - 1175688 * q^66 + 658872 * q^67 + 2907968 * q^68 - 479574 * q^69 + 367696 * q^70 + 191640 * q^71 - 1492992 * q^72 + 49572 * q^73 + 4816648 * q^74 - 1753002 * q^75 - 716416 * q^76 - 1866949 * q^77 - 1898208 * q^78 + 131485 * q^79 - 548864 * q^80 + 2125764 * q^81 + 4774512 * q^82 + 20201469 * q^83 - 2370816 * q^84 + 10179117 * q^85 + 5581808 * q^86 + 674460 * q^87 + 2786816 * q^88 + 13736753 * q^89 + 781488 * q^90 - 3014284 * q^91 + 1136768 * q^92 + 416313 * q^93 + 1904776 * q^94 + 21017342 * q^95 + 3538944 * q^96 + 572361 * q^97 - 3764768 * q^98 - 3967947 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−301.420	−1.07839	−0.539197	−	0.842180i	$-0.681272\pi$
$5$	−301.420	−1.07839	−0.539197	+	0.842180i	$0.681272\pi$
$6$	216.000	0.408248
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	2411.36	0.762539
$11$	−2295.22	−0.519935	−0.259968	−	0.965617i	$-0.583712\pi$
$11$	−2295.22	−0.519935	−0.259968	+	0.965617i	$0.583712\pi$
$12$	−1728.00	−0.288675
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−2744.00	−0.267261
$15$	8138.34	0.622611
$16$	4096.00	0.250000
$17$	−2505.49	−0.123686	−0.0618432	−	0.998086i	$-0.519698\pi$
$17$	−2505.49	−0.123686	−0.0618432	+	0.998086i	$0.519698\pi$
$18$	−5832.00	−0.235702
$19$	−4171.46	−0.139525	−0.0697623	−	0.997564i	$-0.522224\pi$
$19$	−4171.46	−0.139525	−0.0697623	+	0.997564i	$0.522224\pi$
$20$	−19290.9	−0.539197
$21$	−9261.00	−0.218218
$22$	18361.7	0.367650
$23$	30284.2	0.519001	0.259501	−	0.965743i	$-0.416442\pi$
$23$	30284.2	0.519001	0.259501	+	0.965743i	$0.416442\pi$
$24$	13824.0	0.204124
$25$	12729.0	0.162932
$26$	17576.0	0.196116
$27$	−19683.0	−0.192450
$28$	21952.0	0.188982
$29$	129054.	0.982607	0.491303	−	0.870989i	$-0.336521\pi$
$29$	129054.	0.982607	0.491303	+	0.870989i	$0.336521\pi$
$30$	−65106.7	−0.440252
$31$	−193346.	−1.16565	−0.582826	−	0.812597i	$-0.698053\pi$
$31$	−193346.	−1.16565	−0.582826	+	0.812597i	$0.698053\pi$
$32$	−32768.0	−0.176777
$33$	61970.9	0.300185
$34$	20044.0	0.0874596
$35$	−103387.	−0.407594
$36$	46656.0	0.166667
$37$	−129293.	−0.419631	−0.209815	−	0.977741i	$-0.567286\pi$
$37$	−129293.	−0.419631	−0.209815	+	0.977741i	$0.567286\pi$
$38$	33371.7	0.0986588
$39$	59319.0	0.160128
$40$	154327.	0.381270
$41$	−310763.	−0.704184	−0.352092	−	0.935965i	$-0.614530\pi$
$41$	−310763.	−0.704184	−0.352092	+	0.935965i	$0.614530\pi$
$42$	74088.0	0.154303
$43$	240878.	0.462017	0.231008	−	0.972952i	$-0.425798\pi$
$43$	240878.	0.462017	0.231008	+	0.972952i	$0.425798\pi$
$44$	−146894.	−0.259968
$45$	−219735.	−0.359464
$46$	−242273.	−0.366989
$47$	575985.	0.809224	0.404612	−	0.914489i	$-0.367407\pi$
$47$	575985.	0.809224	0.404612	+	0.914489i	$0.367407\pi$
$48$	−110592.	−0.144338
$49$	117649.	0.142857
$50$	−101832.	−0.115210
$51$	67648.4	0.0714104
$52$	−140608.	−0.138675
$53$	150363.	0.138732	0.0693660	−	0.997591i	$-0.477902\pi$
$53$	150363.	0.138732	0.0693660	+	0.997591i	$0.477902\pi$
$54$	157464.	0.136083
$55$	691824.	0.560695
$56$	−175616.	−0.133631
$57$	112630.	0.0805546
$58$	−1.03243e6	−0.694808
$59$	2.69804e6	1.71028	0.855139	−	0.518399i	$-0.173472\pi$
$59$	2.69804e6	1.71028	0.855139	+	0.518399i	$0.173472\pi$
$60$	520854.	0.311305
$61$	−804145.	−0.453607	−0.226803	−	0.973941i	$-0.572828\pi$
$61$	−804145.	−0.453607	−0.226803	+	0.973941i	$0.572828\pi$
$62$	1.54677e6	0.824241
$63$	250047.	0.125988
$64$	262144.	0.125000
$65$	662220.	0.299092
$66$	−495767.	−0.212263
$67$	−3.80152e6	−1.54417	−0.772086	−	0.635518i	$-0.780786\pi$
$67$	−3.80152e6	−1.54417	−0.772086	+	0.635518i	$0.780786\pi$
$68$	−160352.	−0.0618432
$69$	−817673.	−0.299646
$70$	827097.	0.288213
$71$	3.76508e6	1.24845	0.624223	−	0.781246i	$-0.285416\pi$
$71$	3.76508e6	1.24845	0.624223	+	0.781246i	$0.285416\pi$
$72$	−373248.	−0.117851
$73$	5.02926e6	1.51312	0.756561	−	0.653923i	$-0.226878\pi$
$73$	5.02926e6	1.51312	0.756561	+	0.653923i	$0.226878\pi$
$74$	1.03434e6	0.296724
$75$	−343684.	−0.0940687
$76$	−266974.	−0.0697623
$77$	−787259.	−0.196517
$78$	−474552.	−0.113228
$79$	−6.27040e6	−1.43087	−0.715435	−	0.698679i	$-0.753772\pi$
$79$	−6.27040e6	−1.43087	−0.715435	+	0.698679i	$0.753772\pi$
$80$	−1.23462e6	−0.269598
$81$	531441.	0.111111
$82$	2.48610e6	0.497933
$83$	3.15204e6	0.605089	0.302544	−	0.953135i	$-0.402164\pi$
$83$	3.15204e6	0.605089	0.302544	+	0.953135i	$0.402164\pi$
$84$	−592704.	−0.109109
$85$	755206.	0.133383
$86$	−1.92702e6	−0.326695
$87$	−3.48447e6	−0.567308
$88$	1.17515e6	0.183825
$89$	1.23808e7	1.86159	0.930793	−	0.365546i	$-0.119118\pi$
$89$	1.23808e7	1.86159	0.930793	+	0.365546i	$0.119118\pi$
$90$	1.75788e6	0.254180
$91$	−753571.	−0.104828
$92$	1.93819e6	0.259501
$93$	5.22034e6	0.672990
$94$	−4.60788e6	−0.572207
$95$	1.25736e6	0.150462
$96$	884736.	0.102062
$97$	4.74801e6	0.528215	0.264108	−	0.964493i	$-0.414923\pi$
$97$	4.74801e6	0.528215	0.264108	+	0.964493i	$0.414923\pi$
$98$	−941192.	−0.101015
$99$	−1.67321e6	−0.173312
$100$	814659.	0.0814659
$101$	−5.55210e6	−0.536207	−0.268104	−	0.963390i	$-0.586397\pi$
$101$	−5.55210e6	−0.536207	−0.268104	+	0.963390i	$0.586397\pi$
$102$	−541187.	−0.0504948
$103$	5.27426e6	0.475589	0.237794	−	0.971316i	$-0.423576\pi$
$103$	5.27426e6	0.475589	0.237794	+	0.971316i	$0.423576\pi$
$104$	1.12486e6	0.0980581
$105$	2.79145e6	0.235325
$106$	−1.20291e6	−0.0980983
$107$	6.95730e6	0.549032	0.274516	−	0.961583i	$-0.411482\pi$
$107$	6.95730e6	0.549032	0.274516	+	0.961583i	$0.411482\pi$
$108$	−1.25971e6	−0.0962250
$109$	1.53509e7	1.13538	0.567691	−	0.823242i	$-0.307837\pi$
$109$	1.53509e7	1.13538	0.567691	+	0.823242i	$0.307837\pi$
$110$	−5.53460e6	−0.396471
$111$	3.49090e6	0.242274
$112$	1.40493e6	0.0944911
$113$	−1.73484e7	−1.13106	−0.565531	−	0.824727i	$-0.691329\pi$
$113$	−1.73484e7	−1.13106	−0.565531	+	0.824727i	$0.691329\pi$
$114$	−901036.	−0.0569607
$115$	−9.12826e6	−0.559687
$116$	8.25948e6	0.491303
$117$	−1.60161e6	−0.0924500
$118$	−2.15843e7	−1.20935
$119$	−859385.	−0.0467491
$120$	−4.16683e6	−0.220126
$121$	−1.42191e7	−0.729667
$122$	6.43316e6	0.320749
$123$	8.39060e6	0.406561
$124$	−1.23741e7	−0.582826
$125$	1.97117e7	0.902689
$126$	−2.00038e6	−0.0890871
$127$	−3.34024e7	−1.44699	−0.723493	−	0.690332i	$-0.757465\pi$
$127$	−3.34024e7	−1.44699	−0.723493	+	0.690332i	$0.757465\pi$
$128$	−2.09715e6	−0.0883883
$129$	−6.50371e6	−0.266745
$130$	−5.29776e6	−0.211490
$131$	3.05908e7	1.18889	0.594444	−	0.804137i	$-0.297372\pi$
$131$	3.05908e7	1.18889	0.594444	+	0.804137i	$0.297372\pi$
$132$	3.96614e6	0.150092
$133$	−1.43081e6	−0.0527354
$134$	3.04122e7	1.09189
$135$	5.93285e6	0.207537
$136$	1.28281e6	0.0437298
$137$	−9.71099e6	−0.322657	−0.161329	−	0.986901i	$-0.551578\pi$
$137$	−9.71099e6	−0.322657	−0.161329	+	0.986901i	$0.551578\pi$
$138$	6.54138e6	0.211881
$139$	4.87426e7	1.53942	0.769709	−	0.638395i	$-0.220401\pi$
$139$	4.87426e7	1.53942	0.769709	+	0.638395i	$0.220401\pi$
$140$	−6.61677e6	−0.203797
$141$	−1.55516e7	−0.467205
$142$	−3.01206e7	−0.882785
$143$	5.04259e6	0.144204
$144$	2.98598e6	0.0833333
$145$	−3.88996e7	−1.05964
$146$	−4.02341e7	−1.06994
$147$	−3.17652e6	−0.0824786
$148$	−8.27472e6	−0.209815
$149$	1.62427e7	0.402259	0.201129	−	0.979565i	$-0.435539\pi$
$149$	1.62427e7	0.402259	0.201129	+	0.979565i	$0.435539\pi$
$150$	2.74947e6	0.0665166
$151$	1.98316e7	0.468748	0.234374	−	0.972147i	$-0.424696\pi$
$151$	1.98316e7	0.468748	0.234374	+	0.972147i	$0.424696\pi$
$152$	2.13579e6	0.0493294
$153$	−1.82651e6	−0.0412288
$154$	6.29808e6	0.138959
$155$	5.82783e7	1.25703
$156$	3.79642e6	0.0800641
$157$	3.19144e7	0.658170	0.329085	−	0.944300i	$-0.393260\pi$
$157$	3.19144e7	0.658170	0.329085	+	0.944300i	$0.393260\pi$
$158$	5.01632e7	1.01178
$159$	−4.05981e6	−0.0800969
$160$	9.87693e6	0.190635
$161$	1.03875e7	0.196164
$162$	−4.25153e6	−0.0785674
$163$	6.01980e7	1.08874	0.544372	−	0.838844i	$-0.316768\pi$
$163$	6.01980e7	1.08874	0.544372	+	0.838844i	$0.316768\pi$
$164$	−1.98888e7	−0.352092
$165$	−1.86793e7	−0.323717
$166$	−2.52164e7	−0.427862
$167$	−2.09325e7	−0.347787	−0.173894	−	0.984764i	$-0.555635\pi$
$167$	−2.09325e7	−0.347787	−0.173894	+	0.984764i	$0.555635\pi$
$168$	4.74163e6	0.0771517
$169$	4.82681e6	0.0769231
$170$	−6.04165e6	−0.0943158
$171$	−3.04100e6	−0.0465082
$172$	1.54162e7	0.231008
$173$	8.59130e7	1.26153	0.630765	−	0.775974i	$-0.282741\pi$
$173$	8.59130e7	1.26153	0.630765	+	0.775974i	$0.282741\pi$
$174$	2.78757e7	0.401148
$175$	4.36606e6	0.0615824
$176$	−9.40121e6	−0.129984
$177$	−7.28471e7	−0.987429
$178$	−9.90463e7	−1.31634
$179$	−9.53721e6	−0.124290	−0.0621449	−	0.998067i	$-0.519794\pi$
$179$	−9.53721e6	−0.124290	−0.0621449	+	0.998067i	$0.519794\pi$
$180$	−1.40631e7	−0.179732
$181$	−1.10261e8	−1.38213	−0.691063	−	0.722795i	$-0.742857\pi$
$181$	−1.10261e8	−1.38213	−0.691063	+	0.722795i	$0.742857\pi$
$182$	6.02857e6	0.0741249
$183$	2.17119e7	0.261890
$184$	−1.55055e7	−0.183495
$185$	3.89714e7	0.452527
$186$	−4.17627e7	−0.475876
$187$	5.75065e6	0.0643090
$188$	3.68630e7	0.404612
$189$	−6.75127e6	−0.0727393
$190$	−1.00589e7	−0.106393
$191$	−1.08147e6	−0.0112304	−0.00561522	−	0.999984i	$-0.501787\pi$
$191$	−1.08147e6	−0.0112304	−0.00561522	+	0.999984i	$0.501787\pi$
$192$	−7.07789e6	−0.0721688
$193$	3.22334e7	0.322742	0.161371	−	0.986894i	$-0.448408\pi$
$193$	3.22334e7	0.322742	0.161371	+	0.986894i	$0.448408\pi$
$194$	−3.79841e7	−0.373505
$195$	−1.78799e7	−0.172681
$196$	7.52954e6	0.0714286
$197$	−1.71630e8	−1.59941	−0.799707	−	0.600390i	$-0.795012\pi$
$197$	−1.71630e8	−1.59941	−0.799707	+	0.600390i	$0.795012\pi$
$198$	1.33857e7	0.122550
$199$	−6.39876e7	−0.575586	−0.287793	−	0.957693i	$-0.592921\pi$
$199$	−6.39876e7	−0.575586	−0.287793	+	0.957693i	$0.592921\pi$
$200$	−6.51727e6	−0.0576051
$201$	1.02641e8	0.891528
$202$	4.44168e7	0.379156
$203$	4.42656e7	0.371390
$204$	4.32949e6	0.0357052
$205$	9.36702e7	0.759387
$206$	−4.21941e7	−0.336292
$207$	2.20772e7	0.173000
$208$	−8.99891e6	−0.0693375
$209$	9.57442e6	0.0725438
$210$	−2.23316e7	−0.166400
$211$	−1.25208e8	−0.917576	−0.458788	−	0.888546i	$-0.651716\pi$
$211$	−1.25208e8	−0.917576	−0.458788	+	0.888546i	$0.651716\pi$
$212$	9.62326e6	0.0693660
$213$	−1.01657e8	−0.720791
$214$	−5.56584e7	−0.388224
$215$	−7.26055e7	−0.498236
$216$	1.00777e7	0.0680414
$217$	−6.63177e7	−0.440575
$218$	−1.22807e8	−0.802836
$219$	−1.35790e8	−0.873601
$220$	4.42768e7	0.280347
$221$	5.50457e6	0.0343045
$222$	−2.79272e7	−0.171314
$223$	−4.57424e6	−0.0276218	−0.0138109	−	0.999905i	$-0.504396\pi$
$223$	−4.57424e6	−0.0276218	−0.0138109	+	0.999905i	$0.504396\pi$
$224$	−1.12394e7	−0.0668153
$225$	9.27948e6	0.0543106
$226$	1.38788e8	0.799781
$227$	−2.24534e8	−1.27406	−0.637032	−	0.770838i	$-0.719838\pi$
$227$	−2.24534e8	−1.27406	−0.637032	+	0.770838i	$0.719838\pi$
$228$	7.20829e6	0.0402773
$229$	−2.38349e8	−1.31156	−0.655782	−	0.754950i	$-0.727661\pi$
$229$	−2.38349e8	−1.31156	−0.655782	+	0.754950i	$0.727661\pi$
$230$	7.30261e7	0.395759
$231$	2.12560e7	0.113459
$232$	−6.60758e7	−0.347404
$233$	1.58840e7	0.0822648	0.0411324	−	0.999154i	$-0.486903\pi$
$233$	1.58840e7	0.0822648	0.0411324	+	0.999154i	$0.486903\pi$
$234$	1.28129e7	0.0653720
$235$	−1.73613e8	−0.872661
$236$	1.72675e8	0.855139
$237$	1.69301e8	0.826114
$238$	6.87508e6	0.0330566
$239$	3.23552e8	1.53303	0.766515	−	0.642226i	$-0.221989\pi$
$239$	3.23552e8	1.53303	0.766515	+	0.642226i	$0.221989\pi$
$240$	3.33346e7	0.155653
$241$	−5.99123e7	−0.275713	−0.137856	−	0.990452i	$-0.544021\pi$
$241$	−5.99123e7	−0.275713	−0.137856	+	0.990452i	$0.544021\pi$
$242$	1.13753e8	0.515953
$243$	−1.43489e7	−0.0641500
$244$	−5.14653e7	−0.226803
$245$	−3.54618e7	−0.154056
$246$	−6.71248e7	−0.287482
$247$	9.16471e6	0.0386972
$248$	9.89931e7	0.412120
$249$	−8.51052e7	−0.349348
$250$	−1.57693e8	−0.638297
$251$	−4.01886e8	−1.60415	−0.802075	−	0.597223i	$-0.796271\pi$
$251$	−4.01886e8	−1.60415	−0.802075	+	0.597223i	$0.796271\pi$
$252$	1.60030e7	0.0629941
$253$	−6.95088e7	−0.269847
$254$	2.67219e8	1.02317
$255$	−2.03906e7	−0.0770085
$256$	1.67772e7	0.0625000
$257$	−2.83420e8	−1.04151	−0.520757	−	0.853705i	$-0.674350\pi$
$257$	−2.83420e8	−1.04151	−0.520757	+	0.853705i	$0.674350\pi$
$258$	5.20297e7	0.188618
$259$	−4.43473e7	−0.158606
$260$	4.23821e7	0.149546
$261$	9.40806e7	0.327536
$262$	−2.44726e8	−0.840671
$263$	−2.22408e8	−0.753885	−0.376943	−	0.926237i	$-0.623025\pi$
$263$	−2.22408e8	−0.753885	−0.376943	+	0.926237i	$0.623025\pi$
$264$	−3.17291e7	−0.106131
$265$	−4.53225e7	−0.149608
$266$	1.14465e7	0.0372895
$267$	−3.34281e8	−1.07479
$268$	−2.43297e8	−0.772086
$269$	3.30005e8	1.03368	0.516842	−	0.856081i	$-0.327108\pi$
$269$	3.30005e8	1.03368	0.516842	+	0.856081i	$0.327108\pi$
$270$	−4.74628e7	−0.146751
$271$	1.40376e8	0.428450	0.214225	−	0.976784i	$-0.431277\pi$
$271$	1.40376e8	0.428450	0.214225	+	0.976784i	$0.431277\pi$
$272$	−1.02625e7	−0.0309216
$273$	2.03464e7	0.0605228
$274$	7.76880e7	0.228153
$275$	−2.92159e7	−0.0847140
$276$	−5.23311e7	−0.149823
$277$	−3.10343e8	−0.877329	−0.438664	−	0.898651i	$-0.644548\pi$
$277$	−3.10343e8	−0.877329	−0.438664	+	0.898651i	$0.644548\pi$
$278$	−3.89940e8	−1.08853
$279$	−1.40949e8	−0.388551
$280$	5.29342e7	0.144106
$281$	−5.68523e8	−1.52854	−0.764269	−	0.644898i	$-0.776900\pi$
$281$	−5.68523e8	−1.52854	−0.764269	+	0.644898i	$0.776900\pi$
$282$	1.24413e8	0.330364
$283$	−3.34050e8	−0.876110	−0.438055	−	0.898948i	$-0.644332\pi$
$283$	−3.34050e8	−0.876110	−0.438055	+	0.898948i	$0.644332\pi$
$284$	2.40965e8	0.624223
$285$	−3.39488e7	−0.0868695
$286$	−4.03407e7	−0.101968
$287$	−1.06592e8	−0.266156
$288$	−2.38879e7	−0.0589256
$289$	−4.04061e8	−0.984702
$290$	3.11197e8	0.749276
$291$	−1.28196e8	−0.304965
$292$	3.21873e8	0.756561
$293$	−2.84950e8	−0.661809	−0.330904	−	0.943664i	$-0.607354\pi$
$293$	−2.84950e8	−0.661809	−0.330904	+	0.943664i	$0.607354\pi$
$294$	2.54122e7	0.0583212
$295$	−8.13244e8	−1.84435
$296$	6.61978e7	0.148362
$297$	4.51768e7	0.100062
$298$	−1.29941e8	−0.284440
$299$	−6.65344e7	−0.143945
$300$	−2.19958e7	−0.0470344
$301$	8.26212e7	0.174626
$302$	−1.58653e8	−0.331455
$303$	1.49907e8	0.309579
$304$	−1.70863e7	−0.0348812
$305$	2.42385e8	0.489167
$306$	1.46120e7	0.0291532
$307$	1.62176e8	0.319892	0.159946	−	0.987126i	$-0.448868\pi$
$307$	1.62176e8	0.319892	0.159946	+	0.987126i	$0.448868\pi$
$308$	−5.03846e7	−0.0982586
$309$	−1.42405e8	−0.274581
$310$	−4.66227e8	−0.888856
$311$	−1.02220e9	−1.92697	−0.963487	−	0.267754i	$-0.913719\pi$
$311$	−1.02220e9	−1.92697	−0.963487	+	0.267754i	$0.913719\pi$
$312$	−3.03713e7	−0.0566139
$313$	−8.77870e7	−0.161817	−0.0809087	−	0.996722i	$-0.525782\pi$
$313$	−8.77870e7	−0.161817	−0.0809087	+	0.996722i	$0.525782\pi$
$314$	−2.55315e8	−0.465397
$315$	−7.53692e7	−0.135865
$316$	−4.01306e8	−0.715435
$317$	−6.49324e8	−1.14486	−0.572432	−	0.819952i	$-0.694000\pi$
$317$	−6.49324e8	−1.14486	−0.572432	+	0.819952i	$0.694000\pi$
$318$	3.24785e7	0.0566371
$319$	−2.96208e8	−0.510892
$320$	−7.90155e7	−0.134799
$321$	−1.87847e8	−0.316984
$322$	−8.30998e7	−0.138709
$323$	1.04516e7	0.0172573
$324$	3.40122e7	0.0555556
$325$	−2.79657e7	−0.0451892
$326$	−4.81584e8	−0.769858
$327$	−4.14475e8	−0.655513
$328$	1.59111e8	0.248967
$329$	1.97563e8	0.305858
$330$	1.49434e8	0.228903
$331$	6.10784e8	0.925741	0.462871	−	0.886426i	$-0.346819\pi$
$331$	6.10784e8	0.925741	0.462871	+	0.886426i	$0.346819\pi$
$332$	2.01731e8	0.302544
$333$	−9.42542e7	−0.139877
$334$	1.67460e8	0.245923
$335$	1.14585e9	1.66522
$336$	−3.79331e7	−0.0545545
$337$	3.38483e8	0.481761	0.240881	−	0.970555i	$-0.422564\pi$
$337$	3.38483e8	0.481761	0.240881	+	0.970555i	$0.422564\pi$
$338$	−3.86145e7	−0.0543928
$339$	4.68408e8	0.653018
$340$	4.83332e7	0.0666913
$341$	4.43771e8	0.606064
$342$	2.43280e7	0.0328863
$343$	4.03536e7	0.0539949
$344$	−1.23330e8	−0.163348
$345$	2.46463e8	0.323136
$346$	−6.87304e8	−0.892036
$347$	3.39032e8	0.435599	0.217800	−	0.975993i	$-0.430112\pi$
$347$	3.39032e8	0.435599	0.217800	+	0.975993i	$0.430112\pi$
$348$	−2.23006e8	−0.283654
$349$	−9.19558e8	−1.15795	−0.578975	−	0.815345i	$-0.696547\pi$
$349$	−9.19558e8	−1.15795	−0.578975	+	0.815345i	$0.696547\pi$
$350$	−3.49285e7	−0.0435454
$351$	4.32436e7	0.0533761
$352$	7.52097e7	0.0919125
$353$	−7.99684e8	−0.967625	−0.483812	−	0.875172i	$-0.660748\pi$
$353$	−7.99684e8	−0.967625	−0.483812	+	0.875172i	$0.660748\pi$
$354$	5.82777e8	0.698218
$355$	−1.13487e9	−1.34632
$356$	7.92370e8	0.930793
$357$	2.32034e7	0.0269906
$358$	7.62977e7	0.0878862
$359$	4.60879e8	0.525722	0.262861	−	0.964834i	$-0.415334\pi$
$359$	4.60879e8	0.525722	0.262861	+	0.964834i	$0.415334\pi$
$360$	1.12504e8	0.127090
$361$	−8.76471e8	−0.980533
$362$	8.82089e8	0.977311
$363$	3.83917e8	0.421274
$364$	−4.82285e7	−0.0524142
$365$	−1.51592e9	−1.63174
$366$	−1.73695e8	−0.185184
$367$	1.28257e9	1.35441	0.677207	−	0.735793i	$-0.263190\pi$
$367$	1.28257e9	1.35441	0.677207	+	0.735793i	$0.263190\pi$
$368$	1.24044e8	0.129750
$369$	−2.26546e8	−0.234728
$370$	−3.11771e8	−0.319985
$371$	5.15746e7	0.0524358
$372$	3.34102e8	0.336495
$373$	7.83717e8	0.781949	0.390974	−	0.920402i	$-0.372138\pi$
$373$	7.83717e8	0.781949	0.390974	+	0.920402i	$0.372138\pi$
$374$	−4.60052e7	−0.0454733
$375$	−5.32215e8	−0.521168
$376$	−2.94904e8	−0.286104
$377$	−2.83532e8	−0.272526
$378$	5.40102e7	0.0514344
$379$	−3.46477e7	−0.0326917	−0.0163458	−	0.999866i	$-0.505203\pi$
$379$	−3.46477e7	−0.0326917	−0.0163458	+	0.999866i	$0.505203\pi$
$380$	8.04712e7	0.0752312
$381$	9.01864e8	0.835418
$382$	8.65175e6	0.00794113
$383$	4.14386e8	0.376886	0.188443	−	0.982084i	$-0.439656\pi$
$383$	4.14386e8	0.376886	0.188443	+	0.982084i	$0.439656\pi$
$384$	5.66231e7	0.0510310
$385$	2.37296e8	0.211923
$386$	−2.57867e8	−0.228213
$387$	1.75600e8	0.154006
$388$	3.03873e8	0.264108
$389$	−1.65848e9	−1.42853	−0.714263	−	0.699878i	$-0.753238\pi$
$389$	−1.65848e9	−1.42853	−0.714263	+	0.699878i	$0.753238\pi$
$390$	1.43039e8	0.122104
$391$	−7.58769e7	−0.0641934
$392$	−6.02363e7	−0.0505076
$393$	−8.25951e8	−0.686405
$394$	1.37304e9	1.13096
$395$	1.89002e9	1.54304
$396$	−1.07086e8	−0.0866559
$397$	1.87378e9	1.50298	0.751489	−	0.659746i	$-0.229336\pi$
$397$	1.87378e9	1.50298	0.751489	+	0.659746i	$0.229336\pi$
$398$	5.11901e8	0.407001
$399$	3.86319e7	0.0304468
$400$	5.21382e7	0.0407330
$401$	1.87081e9	1.44886	0.724428	−	0.689350i	$-0.242104\pi$
$401$	1.87081e9	1.44886	0.724428	+	0.689350i	$0.242104\pi$
$402$	−8.21128e8	−0.630405
$403$	4.24781e8	0.323294
$404$	−3.55334e8	−0.268104
$405$	−1.60187e8	−0.119821
$406$	−3.54125e8	−0.262613
$407$	2.96754e8	0.218181
$408$	−3.46360e7	−0.0252474
$409$	−2.07046e9	−1.49636	−0.748180	−	0.663496i	$-0.769072\pi$
$409$	−2.07046e9	−1.49636	−0.748180	+	0.663496i	$0.769072\pi$
$410$	−7.49362e8	−0.536968
$411$	2.62197e8	0.186286
$412$	3.37553e8	0.237794
$413$	9.25428e8	0.646424
$414$	−1.76617e8	−0.122330
$415$	−9.50089e8	−0.652523
$416$	7.19913e7	0.0490290
$417$	−1.31605e9	−0.888783
$418$	−7.65953e7	−0.0512962
$419$	−1.20695e9	−0.801565	−0.400782	−	0.916173i	$-0.631262\pi$
$419$	−1.20695e9	−0.801565	−0.400782	+	0.916173i	$0.631262\pi$
$420$	1.78653e8	0.117662
$421$	7.37872e8	0.481941	0.240970	−	0.970532i	$-0.422534\pi$
$421$	7.37872e8	0.481941	0.240970	+	0.970532i	$0.422534\pi$
$422$	1.00166e9	0.648824
$423$	4.19893e8	0.269741
$424$	−7.69860e7	−0.0490492
$425$	−3.18926e7	−0.0201525
$426$	8.13257e8	0.509676
$427$	−2.75822e8	−0.171447
$428$	4.45267e8	0.274516
$429$	−1.36150e8	−0.0832563
$430$	5.80844e8	0.352306
$431$	−1.57778e9	−0.949242	−0.474621	−	0.880190i	$-0.657415\pi$
$431$	−1.57778e9	−0.949242	−0.474621	+	0.880190i	$0.657415\pi$
$432$	−8.06216e7	−0.0481125
$433$	1.63615e9	0.968533	0.484266	−	0.874921i	$-0.339087\pi$
$433$	1.63615e9	0.968533	0.484266	+	0.874921i	$0.339087\pi$
$434$	5.30541e8	0.311534
$435$	1.05029e9	0.611781
$436$	9.82459e8	0.567691
$437$	−1.26329e8	−0.0724135
$438$	1.08632e9	0.617729
$439$	9.61794e8	0.542571	0.271285	−	0.962499i	$-0.412551\pi$
$439$	9.61794e8	0.542571	0.271285	+	0.962499i	$0.412551\pi$
$440$	−3.54214e8	−0.198236
$441$	8.57661e7	0.0476190
$442$	−4.40366e7	−0.0242569
$443$	−4.40650e8	−0.240814	−0.120407	−	0.992725i	$-0.538420\pi$
$443$	−4.40650e8	−0.240814	−0.120407	+	0.992725i	$0.538420\pi$
$444$	2.23417e8	0.121137
$445$	−3.73182e9	−2.00752
$446$	3.65939e7	0.0195315
$447$	−4.38552e8	−0.232244
$448$	8.99154e7	0.0472456
$449$	−1.03917e9	−0.541781	−0.270891	−	0.962610i	$-0.587318\pi$
$449$	−1.03917e9	−0.541781	−0.270891	+	0.962610i	$0.587318\pi$
$450$	−7.42358e7	−0.0384034
$451$	7.13269e8	0.366130
$452$	−1.11030e9	−0.565531
$453$	−5.35454e8	−0.270632
$454$	1.79627e9	0.900899
$455$	2.27141e8	0.113046
$456$	−5.76663e7	−0.0284803
$457$	−2.60785e9	−1.27813	−0.639067	−	0.769151i	$-0.720679\pi$
$457$	−2.60785e9	−1.27813	−0.639067	+	0.769151i	$0.720679\pi$
$458$	1.90679e9	0.927416
$459$	4.93157e7	0.0238035
$460$	−5.84209e8	−0.279844
$461$	1.57639e9	0.749394	0.374697	−	0.927147i	$-0.377747\pi$
$461$	1.57639e9	0.749394	0.374697	+	0.927147i	$0.377747\pi$
$462$	−1.70048e8	−0.0802278
$463$	−1.59307e7	−0.00745935	−0.00372967	−	0.999993i	$-0.501187\pi$
$463$	−1.59307e7	−0.00745935	−0.00372967	+	0.999993i	$0.501187\pi$
$464$	5.28607e8	0.245652
$465$	−1.57352e9	−0.725748
$466$	−1.27072e8	−0.0581700
$467$	3.43135e8	0.155904	0.0779518	−	0.996957i	$-0.475162\pi$
$467$	3.43135e8	0.155904	0.0779518	+	0.996957i	$0.475162\pi$
$468$	−1.02503e8	−0.0462250
$469$	−1.30392e9	−0.583642
$470$	1.38891e9	0.617065
$471$	−8.61690e8	−0.379995
$472$	−1.38140e9	−0.604675
$473$	−5.52867e8	−0.240219
$474$	−1.35441e9	−0.584150
$475$	−5.30988e7	−0.0227330
$476$	−5.50006e7	−0.0233745
$477$	1.09615e8	0.0462440
$478$	−2.58841e9	−1.08402
$479$	−2.08112e9	−0.865212	−0.432606	−	0.901583i	$-0.642406\pi$
$479$	−2.08112e9	−0.865212	−0.432606	+	0.901583i	$0.642406\pi$
$480$	−2.66677e8	−0.110063
$481$	2.84056e8	0.116385
$482$	4.79299e8	0.194958
$483$	−2.80462e8	−0.113255
$484$	−9.10026e8	−0.364834
$485$	−1.43115e9	−0.569624
$486$	1.14791e8	0.0453609
$487$	−2.71466e9	−1.06503	−0.532517	−	0.846419i	$-0.678754\pi$
$487$	−2.71466e9	−1.06503	−0.532517	+	0.846419i	$0.678754\pi$
$488$	4.11722e8	0.160374
$489$	−1.62535e9	−0.628586
$490$	2.83694e8	0.108934
$491$	−2.36235e9	−0.900655	−0.450327	−	0.892863i	$-0.648693\pi$
$491$	−2.36235e9	−0.900655	−0.450327	+	0.892863i	$0.648693\pi$
$492$	5.36999e8	0.203280
$493$	−3.23345e8	−0.121535
$494$	−7.33177e7	−0.0273630
$495$	5.04340e8	0.186898
$496$	−7.91945e8	−0.291413
$497$	1.29142e9	0.471868
$498$	6.80842e8	0.247026
$499$	1.59920e9	0.576172	0.288086	−	0.957605i	$-0.406981\pi$
$499$	1.59920e9	0.576172	0.288086	+	0.957605i	$0.406981\pi$
$500$	1.26155e9	0.451344
$501$	5.65178e8	0.200795
$502$	3.21509e9	1.13431
$503$	1.70080e9	0.595890	0.297945	−	0.954583i	$-0.403699\pi$
$503$	1.70080e9	0.595890	0.297945	+	0.954583i	$0.403699\pi$
$504$	−1.28024e8	−0.0445435
$505$	1.67351e9	0.578242
$506$	5.56070e8	0.190811
$507$	−1.30324e8	−0.0444116
$508$	−2.13775e9	−0.723493
$509$	3.03696e9	1.02077	0.510384	−	0.859946i	$-0.329503\pi$
$509$	3.03696e9	1.02077	0.510384	+	0.859946i	$0.329503\pi$
$510$	1.63125e8	0.0544532
$511$	1.72504e9	0.571906
$512$	−1.34218e8	−0.0441942
$513$	8.21069e7	0.0268515
$514$	2.26736e9	0.736462
$515$	−1.58977e9	−0.512872
$516$	−4.16237e8	−0.133373
$517$	−1.32201e9	−0.420744
$518$	3.54779e8	0.112151
$519$	−2.31965e9	−0.728345
$520$	−3.39057e8	−0.105745
$521$	3.66735e9	1.13611	0.568054	−	0.822991i	$-0.307696\pi$
$521$	3.66735e9	1.13611	0.568054	+	0.822991i	$0.307696\pi$
$522$	−7.52645e8	−0.231603
$523$	−4.16615e8	−0.127344	−0.0636721	−	0.997971i	$-0.520281\pi$
$523$	−4.16615e8	−0.127344	−0.0636721	+	0.997971i	$0.520281\pi$
$524$	1.95781e9	0.594444
$525$	−1.17884e8	−0.0355546
$526$	1.77926e9	0.533077
$527$	4.84427e8	0.144175
$528$	2.53833e8	0.0750462
$529$	−2.48769e9	−0.730638
$530$	3.62580e8	0.105789
$531$	1.96687e9	0.570093
$532$	−9.15720e7	−0.0263677
$533$	6.82747e8	0.195305
$534$	2.67425e9	0.759990
$535$	−2.09707e9	−0.592072
$536$	1.94638e9	0.545947
$537$	2.57505e8	0.0717588
$538$	−2.64004e9	−0.730924
$539$	−2.70030e8	−0.0742765
$540$	3.79702e8	0.103768
$541$	2.16237e9	0.587137	0.293568	−	0.955938i	$-0.405157\pi$
$541$	2.16237e9	0.587137	0.293568	+	0.955938i	$0.405157\pi$
$542$	−1.12301e9	−0.302960
$543$	2.97705e9	0.797971
$544$	8.21000e7	0.0218649
$545$	−4.62708e9	−1.22439
$546$	−1.62771e8	−0.0427960
$547$	−2.50606e9	−0.654690	−0.327345	−	0.944905i	$-0.606154\pi$
$547$	−2.50606e9	−0.654690	−0.327345	+	0.944905i	$0.606154\pi$
$548$	−6.21504e8	−0.161329
$549$	−5.86221e8	−0.151202
$550$	2.33727e8	0.0599019
$551$	−5.38346e8	−0.137098
$552$	4.18649e8	0.105941
$553$	−2.15075e9	−0.540818
$554$	2.48274e9	0.620365
$555$	−1.05223e9	−0.261267
$556$	3.11952e9	0.769709
$557$	3.60897e9	0.884892	0.442446	−	0.896795i	$-0.354111\pi$
$557$	3.60897e9	0.884892	0.442446	+	0.896795i	$0.354111\pi$
$558$	1.12759e9	0.274747
$559$	−5.29209e8	−0.128140
$560$	−4.23473e8	−0.101899
$561$	−1.55268e8	−0.0371288
$562$	4.54819e9	1.08084
$563$	4.02598e9	0.950807	0.475403	−	0.879768i	$-0.342302\pi$
$563$	4.02598e9	0.950807	0.475403	+	0.879768i	$0.342302\pi$
$564$	−9.95302e8	−0.233603
$565$	5.22917e9	1.21973
$566$	2.67240e9	0.619503
$567$	1.82284e8	0.0419961
$568$	−1.92772e9	−0.441393
$569$	2.99014e9	0.680453	0.340227	−	0.940343i	$-0.389496\pi$
$569$	2.99014e9	0.680453	0.340227	+	0.940343i	$0.389496\pi$
$570$	2.71590e8	0.0614260
$571$	−5.03513e9	−1.13184	−0.565919	−	0.824461i	$-0.691478\pi$
$571$	−5.03513e9	−1.13184	−0.565919	+	0.824461i	$0.691478\pi$
$572$	3.22726e8	0.0721021
$573$	2.91997e7	0.00648390
$574$	8.52734e8	0.188201
$575$	3.85489e8	0.0845618
$576$	1.91103e8	0.0416667
$577$	−6.15391e9	−1.33363	−0.666816	−	0.745222i	$-0.732343\pi$
$577$	−6.15391e9	−1.33363	−0.666816	+	0.745222i	$0.732343\pi$
$578$	3.23249e9	0.696289
$579$	−8.70301e8	−0.186335
$580$	−2.48957e9	−0.529818
$581$	1.08115e9	0.228702
$582$	1.02557e9	0.215643
$583$	−3.45117e8	−0.0721317
$584$	−2.57498e9	−0.534969
$585$	4.82758e8	0.0996975
$586$	2.27960e9	0.467969
$587$	8.30824e9	1.69541	0.847707	−	0.530464i	$-0.177982\pi$
$587$	8.30824e9	1.69541	0.847707	+	0.530464i	$0.177982\pi$
$588$	−2.03297e8	−0.0412393
$589$	8.06536e8	0.162637
$590$	6.50595e9	1.30415
$591$	4.63401e9	0.923423
$592$	−5.29582e8	−0.104908
$593$	2.73958e9	0.539501	0.269751	−	0.962930i	$-0.413059\pi$
$593$	2.73958e9	0.539501	0.269751	+	0.962930i	$0.413059\pi$
$594$	−3.61414e8	−0.0707542
$595$	2.59036e8	0.0504139
$596$	1.03953e9	0.201129
$597$	1.72766e9	0.332315
$598$	5.32275e8	0.101785
$599$	4.35172e9	0.827308	0.413654	−	0.910434i	$-0.364252\pi$
$599$	4.35172e9	0.827308	0.413654	+	0.910434i	$0.364252\pi$
$600$	1.75966e8	0.0332583
$601$	−7.13292e9	−1.34032	−0.670158	−	0.742219i	$-0.733773\pi$
$601$	−7.13292e9	−1.34032	−0.670158	+	0.742219i	$0.733773\pi$
$602$	−6.60969e8	−0.123479
$603$	−2.77131e9	−0.514724
$604$	1.26922e9	0.234374
$605$	4.28594e9	0.786868
$606$	−1.19925e9	−0.218906
$607$	6.80819e9	1.23558	0.617791	−	0.786342i	$-0.288028\pi$
$607$	6.80819e9	1.23558	0.617791	+	0.786342i	$0.288028\pi$
$608$	1.36691e8	0.0246647
$609$	−1.19517e9	−0.214422
$610$	−1.93908e9	−0.345893
$611$	−1.26544e9	−0.224438
$612$	−1.16896e8	−0.0206144
$613$	3.32924e9	0.583758	0.291879	−	0.956455i	$-0.405720\pi$
$613$	3.32924e9	0.583758	0.291879	+	0.956455i	$0.405720\pi$
$614$	−1.29741e9	−0.226198
$615$	−2.52910e9	−0.438432
$616$	4.03077e8	0.0694793
$617$	2.53855e9	0.435098	0.217549	−	0.976049i	$-0.430194\pi$
$617$	2.53855e9	0.435098	0.217549	+	0.976049i	$0.430194\pi$
$618$	1.13924e9	0.194158
$619$	5.90910e9	1.00139	0.500696	−	0.865623i	$-0.333078\pi$
$619$	5.90910e9	1.00139	0.500696	+	0.865623i	$0.333078\pi$
$620$	3.72981e9	0.628516
$621$	−5.96084e8	−0.0998818
$622$	8.17763e9	1.36258
$623$	4.24661e9	0.703614
$624$	2.42971e8	0.0400320
$625$	−6.93594e9	−1.13639
$626$	7.02296e8	0.114422
$627$	−2.58509e8	−0.0418832
$628$	2.04252e9	0.329085
$629$	3.23942e8	0.0519027
$630$	6.02953e8	0.0960709
$631$	−1.05866e9	−0.167747	−0.0838736	−	0.996476i	$-0.526729\pi$
$631$	−1.05866e9	−0.167747	−0.0838736	+	0.996476i	$0.526729\pi$
$632$	3.21044e9	0.505889
$633$	3.38060e9	0.529763
$634$	5.19459e9	0.809541
$635$	1.00681e10	1.56042
$636$	−2.59828e8	−0.0400485
$637$	−2.58475e8	−0.0396214
$638$	2.36966e9	0.361255
$639$	2.74474e9	0.416149
$640$	6.32124e8	0.0953174
$641$	4.56593e9	0.684740	0.342370	−	0.939565i	$-0.388770\pi$
$641$	4.56593e9	0.684740	0.342370	+	0.939565i	$0.388770\pi$
$642$	1.50278e9	0.224141
$643$	−8.82098e8	−0.130851	−0.0654257	−	0.997857i	$-0.520841\pi$
$643$	−8.82098e8	−0.130851	−0.0654257	+	0.997857i	$0.520841\pi$
$644$	6.64798e8	0.0980820
$645$	1.96035e9	0.287656
$646$	−8.36127e7	−0.0122028
$647$	−6.14601e9	−0.892130	−0.446065	−	0.895001i	$-0.647175\pi$
$647$	−6.14601e9	−0.892130	−0.446065	+	0.895001i	$0.647175\pi$
$648$	−2.72098e8	−0.0392837
$649$	−6.19259e9	−0.889234
$650$	2.23726e8	0.0319536
$651$	1.79058e9	0.254366
$652$	3.85267e9	0.544372
$653$	−1.06878e10	−1.50208	−0.751039	−	0.660258i	$-0.770447\pi$
$653$	−1.06878e10	−1.50208	−0.751039	+	0.660258i	$0.770447\pi$
$654$	3.31580e9	0.463518
$655$	−9.22068e9	−1.28209
$656$	−1.27289e9	−0.176046
$657$	3.66633e9	0.504374
$658$	−1.58050e9	−0.216274
$659$	8.22043e9	1.11891	0.559456	−	0.828860i	$-0.311010\pi$
$659$	8.22043e9	1.11891	0.559456	+	0.828860i	$0.311010\pi$
$660$	−1.19547e9	−0.161859
$661$	4.70539e9	0.633710	0.316855	−	0.948474i	$-0.397373\pi$
$661$	4.70539e9	0.633710	0.316855	+	0.948474i	$0.397373\pi$
$662$	−4.88627e9	−0.654598
$663$	−1.48623e8	−0.0198057
$664$	−1.61385e9	−0.213931
$665$	4.31276e8	0.0568695
$666$	7.54034e8	0.0989079
$667$	3.90831e9	0.509974
$668$	−1.33968e9	−0.173894
$669$	1.23504e8	0.0159474
$670$	−9.16684e9	−1.17749
$671$	1.84569e9	0.235846
$672$	3.03464e8	0.0385758
$673$	1.69961e9	0.214930	0.107465	−	0.994209i	$-0.465727\pi$
$673$	1.69961e9	0.214930	0.107465	+	0.994209i	$0.465727\pi$
$674$	−2.70786e9	−0.340656
$675$	−2.50546e8	−0.0313562
$676$	3.08916e8	0.0384615
$677$	−5.86068e9	−0.725918	−0.362959	−	0.931805i	$-0.618233\pi$
$677$	−5.86068e9	−0.725918	−0.362959	+	0.931805i	$0.618233\pi$
$678$	−3.74727e9	−0.461754
$679$	1.62857e9	0.199647
$680$	−3.86666e8	−0.0471579
$681$	6.06241e9	0.735581
$682$	−3.55017e9	−0.428552
$683$	−2.03614e9	−0.244532	−0.122266	−	0.992497i	$-0.539016\pi$
$683$	−2.03614e9	−0.244532	−0.122266	+	0.992497i	$0.539016\pi$
$684$	−1.94624e8	−0.0232541
$685$	2.92709e9	0.347952
$686$	−3.22829e8	−0.0381802
$687$	6.43543e9	0.757232
$688$	9.86636e8	0.115504
$689$	−3.30348e8	−0.0384773
$690$	−1.97170e9	−0.228491
$691$	−1.41281e10	−1.62896	−0.814479	−	0.580193i	$-0.802977\pi$
$691$	−1.41281e10	−1.62896	−0.814479	+	0.580193i	$0.802977\pi$
$692$	5.49843e9	0.630765
$693$	−5.73912e8	−0.0655057
$694$	−2.71225e9	−0.308015
$695$	−1.46920e10	−1.66010
$696$	1.78405e9	0.200574
$697$	7.78615e8	0.0870980
$698$	7.35646e9	0.818795
$699$	−4.28868e8	−0.0474956
$700$	2.79428e8	0.0307912
$701$	1.03325e10	1.13290	0.566451	−	0.824095i	$-0.308316\pi$
$701$	1.03325e10	1.13290	0.566451	+	0.824095i	$0.308316\pi$
$702$	−3.45948e8	−0.0377426
$703$	5.39339e8	0.0585488
$704$	−6.01677e8	−0.0649919
$705$	4.68756e9	0.503831
$706$	6.39747e9	0.684214
$707$	−1.90437e9	−0.202667
$708$	−4.66222e9	−0.493715
$709$	−1.83104e9	−0.192946	−0.0964729	−	0.995336i	$-0.530756\pi$
$709$	−1.83104e9	−0.192946	−0.0964729	+	0.995336i	$0.530756\pi$
$710$	9.07897e9	0.951989
$711$	−4.57112e9	−0.476957
$712$	−6.33896e9	−0.658170
$713$	−5.85532e9	−0.604975
$714$	−1.85627e8	−0.0190852
$715$	−1.51994e9	−0.155509
$716$	−6.10382e8	−0.0621449
$717$	−8.73589e9	−0.885096
$718$	−3.68703e9	−0.371741
$719$	5.65092e8	0.0566980	0.0283490	−	0.999598i	$-0.490975\pi$
$719$	5.65092e8	0.0566980	0.0283490	+	0.999598i	$0.490975\pi$
$720$	−9.00035e8	−0.0898661
$721$	1.80907e9	0.179756
$722$	7.01176e9	0.693341
$723$	1.61763e9	0.159183
$724$	−7.05671e9	−0.691063
$725$	1.64274e9	0.160098
$726$	−3.07134e9	−0.297885
$727$	−8.10488e9	−0.782305	−0.391152	−	0.920326i	$-0.627923\pi$
$727$	−8.10488e9	−0.782305	−0.391152	+	0.920326i	$0.627923\pi$
$728$	3.85828e8	0.0370625
$729$	3.87420e8	0.0370370
$730$	1.21274e10	1.15381
$731$	−6.03519e8	−0.0571452
$732$	1.38956e9	0.130945
$733$	8.54767e9	0.801648	0.400824	−	0.916155i	$-0.368724\pi$
$733$	8.54767e9	0.801648	0.400824	+	0.916155i	$0.368724\pi$
$734$	−1.02606e10	−0.957715
$735$	9.57468e8	0.0889444
$736$	−9.92352e8	−0.0917473
$737$	8.72531e9	0.802869
$738$	1.81237e9	0.165978
$739$	−5.51763e9	−0.502918	−0.251459	−	0.967868i	$-0.580910\pi$
$739$	−5.51763e9	−0.502918	−0.251459	+	0.967868i	$0.580910\pi$
$740$	2.49417e9	0.226263
$741$	−2.47447e8	−0.0223418
$742$	−4.12597e8	−0.0370777
$743$	−4.09024e9	−0.365837	−0.182919	−	0.983128i	$-0.558554\pi$
$743$	−4.09024e9	−0.365837	−0.182919	+	0.983128i	$0.558554\pi$
$744$	−2.67281e9	−0.237938
$745$	−4.89587e9	−0.433793
$746$	−6.26973e9	−0.552921
$747$	2.29784e9	0.201696
$748$	3.68042e8	0.0321545
$749$	2.38635e9	0.207514
$750$	4.25772e9	0.368521
$751$	−1.85394e10	−1.59719	−0.798593	−	0.601872i	$-0.794422\pi$
$751$	−1.85394e10	−1.59719	−0.798593	+	0.601872i	$0.794422\pi$
$752$	2.35923e9	0.202306
$753$	1.08509e10	0.926156
$754$	2.26826e9	0.192705
$755$	−5.97765e9	−0.505494
$756$	−4.32081e8	−0.0363696
$757$	−2.42398e9	−0.203092	−0.101546	−	0.994831i	$-0.532379\pi$
$757$	−2.42398e9	−0.203092	−0.101546	+	0.994831i	$0.532379\pi$
$758$	2.77182e8	0.0231165
$759$	1.87674e9	0.155796
$760$	−6.43770e8	−0.0531965
$761$	3.38141e9	0.278133	0.139066	−	0.990283i	$-0.455590\pi$
$761$	3.38141e9	0.278133	0.139066	+	0.990283i	$0.455590\pi$
$762$	−7.21491e9	−0.590729
$763$	5.26537e9	0.429134
$764$	−6.92140e7	−0.00561522
$765$	5.50545e8	0.0444609
$766$	−3.31509e9	−0.266498
$767$	−5.92760e9	−0.474346
$768$	−4.52985e8	−0.0360844
$769$	−1.00168e10	−0.794305	−0.397152	−	0.917753i	$-0.630002\pi$
$769$	−1.00168e10	−0.794305	−0.397152	+	0.917753i	$0.630002\pi$
$770$	−1.89837e9	−0.149852
$771$	7.65235e9	0.601318
$772$	2.06294e9	0.161371
$773$	2.44386e10	1.90304	0.951520	−	0.307586i	$-0.0995211\pi$
$773$	2.44386e10	1.90304	0.951520	+	0.307586i	$0.0995211\pi$
$774$	−1.40480e9	−0.108898
$775$	−2.46111e9	−0.189922
$776$	−2.43098e9	−0.186752
$777$	1.19738e9	0.0915709
$778$	1.32679e10	1.01012
$779$	1.29634e9	0.0982510
$780$	−1.14432e9	−0.0863406
$781$	−8.64168e9	−0.649112
$782$	6.07015e8	0.0453916
$783$	−2.54018e9	−0.189103
$784$	4.81890e8	0.0357143
$785$	−9.61965e9	−0.709766
$786$	6.60761e9	0.485362
$787$	−1.06895e10	−0.781708	−0.390854	−	0.920453i	$-0.627820\pi$
$787$	−1.06895e10	−0.781708	−0.390854	+	0.920453i	$0.627820\pi$
$788$	−1.09843e10	−0.799707
$789$	6.00501e9	0.435256
$790$	−1.51202e10	−1.09109
$791$	−5.95052e9	−0.427501
$792$	8.56685e8	0.0612750
$793$	1.76671e9	0.125808
$794$	−1.49903e10	−1.06277
$795$	1.22371e9	0.0863760
$796$	−4.09521e9	−0.287793
$797$	4.40043e9	0.307887	0.153944	−	0.988080i	$-0.450803\pi$
$797$	4.40043e9	0.307887	0.153944	+	0.988080i	$0.450803\pi$
$798$	−3.09055e8	−0.0215291
$799$	−1.44313e9	−0.100090
$800$	−4.17106e8	−0.0288026
$801$	9.02559e9	0.620529
$802$	−1.49665e10	−1.02450
$803$	−1.15432e10	−0.786726
$804$	6.56903e9	0.445764
$805$	−3.13099e9	−0.211542
$806$	−3.39825e9	−0.228603
$807$	−8.91013e9	−0.596797
$808$	2.84268e9	0.189578
$809$	1.08820e10	0.722587	0.361294	−	0.932452i	$-0.382335\pi$
$809$	1.08820e10	0.722587	0.361294	+	0.932452i	$0.382335\pi$
$810$	1.28150e9	0.0847266
$811$	−2.41836e10	−1.59202	−0.796009	−	0.605284i	$-0.793059\pi$
$811$	−2.41836e10	−1.59202	−0.796009	+	0.605284i	$0.793059\pi$
$812$	2.83300e9	0.185695
$813$	−3.79015e9	−0.247366
$814$	−2.37403e9	−0.154277
$815$	−1.81449e10	−1.17409
$816$	2.77088e8	0.0178526
$817$	−1.00481e9	−0.0644627
$818$	1.65637e10	1.05809
$819$	−5.49353e8	−0.0349428
$820$	5.99490e9	0.379693
$821$	−1.99408e10	−1.25760	−0.628800	−	0.777567i	$-0.716453\pi$
$821$	−1.99408e10	−1.25760	−0.628800	+	0.777567i	$0.716453\pi$
$822$	−2.09757e9	−0.131724
$823$	1.21207e10	0.757929	0.378965	−	0.925411i	$-0.376280\pi$
$823$	1.21207e10	0.757929	0.378965	+	0.925411i	$0.376280\pi$
$824$	−2.70042e9	−0.168146
$825$	7.88830e8	0.0489097
$826$	−7.40343e9	−0.457091
$827$	−8.07433e9	−0.496406	−0.248203	−	0.968708i	$-0.579840\pi$
$827$	−8.07433e9	−0.496406	−0.248203	+	0.968708i	$0.579840\pi$
$828$	1.41294e9	0.0865002
$829$	1.13985e10	0.694878	0.347439	−	0.937703i	$-0.387051\pi$
$829$	1.13985e10	0.694878	0.347439	+	0.937703i	$0.387051\pi$
$830$	7.60072e9	0.461404
$831$	8.37925e9	0.506526
$832$	−5.75930e8	−0.0346688
$833$	−2.94769e8	−0.0176695
$834$	1.05284e10	0.628465
$835$	6.30948e9	0.375052
$836$	6.12763e8	0.0362719
$837$	3.80563e9	0.224330
$838$	9.65556e9	0.566792
$839$	−2.06454e10	−1.20686	−0.603428	−	0.797417i	$-0.706199\pi$
$839$	−2.06454e10	−1.20686	−0.603428	+	0.797417i	$0.706199\pi$
$840$	−1.42922e9	−0.0831998
$841$	−5.94845e8	−0.0344840
$842$	−5.90298e9	−0.340784
$843$	1.53501e10	0.882502
$844$	−8.01328e9	−0.458788
$845$	−1.45490e9	−0.0829533
$846$	−3.35914e9	−0.190736
$847$	−4.87717e9	−0.275788
$848$	6.15888e8	0.0346830
$849$	9.01934e9	0.505822
$850$	2.55141e8	0.0142499
$851$	−3.91552e9	−0.217789
$852$	−6.50606e9	−0.360396
$853$	1.41173e10	0.778810	0.389405	−	0.921067i	$-0.372681\pi$
$853$	1.41173e10	0.778810	0.389405	+	0.921067i	$0.372681\pi$
$854$	2.20657e9	0.121232
$855$	9.16618e8	0.0501541
$856$	−3.56214e9	−0.194112
$857$	−9.80616e9	−0.532189	−0.266094	−	0.963947i	$-0.585733\pi$
$857$	−9.80616e9	−0.532189	−0.266094	+	0.963947i	$0.585733\pi$
$858$	1.08920e9	0.0588711
$859$	−1.42274e10	−0.765859	−0.382930	−	0.923777i	$-0.625085\pi$
$859$	−1.42274e10	−0.765859	−0.382930	+	0.923777i	$0.625085\pi$
$860$	−4.64675e9	−0.249118
$861$	2.87798e9	0.153665
$862$	1.26223e10	0.671216
$863$	−1.36633e10	−0.723632	−0.361816	−	0.932250i	$-0.617843\pi$
$863$	−1.36633e10	−0.723632	−0.361816	+	0.932250i	$0.617843\pi$
$864$	6.44973e8	0.0340207
$865$	−2.58959e10	−1.36043
$866$	−1.30892e10	−0.684856
$867$	1.09097e10	0.568518
$868$	−4.24433e9	−0.220288
$869$	1.43919e10	0.743960
$870$	−8.40231e9	−0.432595
$871$	8.35194e9	0.428276
$872$	−7.85968e9	−0.401418
$873$	3.46130e9	0.176072
$874$	1.01064e9	0.0512041
$875$	6.76110e9	0.341184
$876$	−8.69056e9	−0.436801
$877$	−2.11030e10	−1.05644	−0.528221	−	0.849107i	$-0.677141\pi$
$877$	−2.11030e10	−1.05644	−0.528221	+	0.849107i	$0.677141\pi$
$878$	−7.69436e9	−0.383656
$879$	7.69366e9	0.382095
$880$	2.83371e9	0.140174
$881$	−1.25515e10	−0.618413	−0.309206	−	0.950995i	$-0.600063\pi$
$881$	−1.25515e10	−0.618413	−0.309206	+	0.950995i	$0.600063\pi$
$882$	−6.86129e8	−0.0336718
$883$	5.83602e9	0.285269	0.142634	−	0.989775i	$-0.454443\pi$
$883$	5.83602e9	0.285269	0.142634	+	0.989775i	$0.454443\pi$
$884$	3.52293e8	0.0171522
$885$	2.19576e10	1.06484
$886$	3.52520e9	0.170281
$887$	−9.50001e9	−0.457079	−0.228540	−	0.973535i	$-0.573395\pi$
$887$	−9.50001e9	−0.457079	−0.228540	+	0.973535i	$0.573395\pi$
$888$	−1.78734e9	−0.0856568
$889$	−1.14570e10	−0.546909
$890$	2.98545e10	1.41953
$891$	−1.21977e9	−0.0577706
$892$	−2.92751e8	−0.0138109
$893$	−2.40270e9	−0.112907
$894$	3.50842e9	0.164222
$895$	2.87471e9	0.134033
$896$	−7.19323e8	−0.0334077
$897$	1.79643e9	0.0831067
$898$	8.31335e9	0.383097
$899$	−2.49521e10	−1.14538
$900$	5.93887e8	0.0271553
$901$	−3.76735e8	−0.0171593
$902$	−5.70615e9	−0.258893
$903$	−2.23077e9	−0.100820
$904$	8.88241e9	0.399891
$905$	3.32349e10	1.49048
$906$	4.28363e9	0.191365
$907$	−3.41798e10	−1.52105	−0.760526	−	0.649307i	$-0.775059\pi$
$907$	−3.41798e10	−1.52105	−0.760526	+	0.649307i	$0.775059\pi$
$908$	−1.43702e10	−0.637032
$909$	−4.04748e9	−0.178736
$910$	−1.81713e9	−0.0799358
$911$	6.63638e9	0.290815	0.145407	−	0.989372i	$-0.453551\pi$
$911$	6.63638e9	0.290815	0.145407	+	0.989372i	$0.453551\pi$
$912$	4.61331e8	0.0201386
$913$	−7.23463e9	−0.314607
$914$	2.08628e10	0.903777
$915$	−6.54440e9	−0.282420
$916$	−1.52543e10	−0.655782
$917$	1.04926e10	0.449358
$918$	−3.94525e8	−0.0168316
$919$	−3.33365e10	−1.41682	−0.708411	−	0.705800i	$-0.750588\pi$
$919$	−3.33365e10	−1.41682	−0.708411	+	0.705800i	$0.750588\pi$
$920$	4.67367e9	0.197879
$921$	−4.37876e9	−0.184690
$922$	−1.26111e10	−0.529902
$923$	−8.27188e9	−0.346257
$924$	1.36038e9	0.0567296
$925$	−1.64577e9	−0.0683712
$926$	1.27445e8	0.00527456
$927$	3.84494e9	0.158530
$928$	−4.22885e9	−0.173702
$929$	−1.30876e10	−0.535555	−0.267778	−	0.963481i	$-0.586289\pi$
$929$	−1.30876e10	−0.535555	−0.267778	+	0.963481i	$0.586289\pi$
$930$	1.25881e10	0.513181
$931$	−4.90769e8	−0.0199321
$932$	1.01658e9	0.0411324
$933$	2.75995e10	1.11254
$934$	−2.74508e9	−0.110241
$935$	−1.73336e9	−0.0693504
$936$	8.20026e8	0.0326860
$937$	2.16895e9	0.0861312	0.0430656	−	0.999072i	$-0.486288\pi$
$937$	2.16895e9	0.0861312	0.0430656	+	0.999072i	$0.486288\pi$
$938$	1.04314e10	0.412697
$939$	2.37025e9	0.0934253
$940$	−1.11113e10	−0.436331
$941$	8.39537e9	0.328455	0.164228	−	0.986422i	$-0.447487\pi$
$941$	8.39537e9	0.328455	0.164228	+	0.986422i	$0.447487\pi$
$942$	6.89352e9	0.268697
$943$	−9.41121e9	−0.365472
$944$	1.10512e10	0.427569
$945$	2.03497e9	0.0784416
$946$	4.42294e9	0.169860
$947$	3.40763e10	1.30385	0.651924	−	0.758284i	$-0.273962\pi$
$947$	3.40763e10	1.30385	0.651924	+	0.758284i	$0.273962\pi$
$948$	1.08352e10	0.413057
$949$	−1.10493e10	−0.419665
$950$	4.24790e8	0.0160747
$951$	1.75317e10	0.660987
$952$	4.40005e8	0.0165283
$953$	−1.11778e10	−0.418340	−0.209170	−	0.977879i	$-0.567076\pi$
$953$	−1.11778e10	−0.418340	−0.209170	+	0.977879i	$0.567076\pi$
$954$	−8.76919e8	−0.0326994
$955$	3.25976e8	0.0121108
$956$	2.07073e10	0.766515
$957$	7.99761e9	0.294964
$958$	1.66489e10	0.611797
$959$	−3.33087e9	−0.121953
$960$	2.13342e9	0.0778263
$961$	9.87004e9	0.358746
$962$	−2.27245e9	−0.0822964
$963$	5.07187e9	0.183011
$964$	−3.83439e9	−0.137856
$965$	−9.71578e9	−0.348042
$966$	2.24369e9	0.0800836
$967$	3.07348e9	0.109304	0.0546522	−	0.998505i	$-0.482595\pi$
$967$	3.07348e9	0.109304	0.0546522	+	0.998505i	$0.482595\pi$
$968$	7.28020e9	0.257976
$969$	−2.82193e8	−0.00996351
$970$	1.14492e10	0.402785
$971$	4.14396e10	1.45261	0.726303	−	0.687374i	$-0.241237\pi$
$971$	4.14396e10	1.45261	0.726303	+	0.687374i	$0.241237\pi$
$972$	−9.18330e8	−0.0320750
$973$	1.67187e10	0.581845
$974$	2.17173e10	0.753093
$975$	7.55075e8	0.0260900
$976$	−3.29378e9	−0.113402
$977$	−2.49761e10	−0.856828	−0.428414	−	0.903583i	$-0.640928\pi$
$977$	−2.49761e10	−0.856828	−0.428414	+	0.903583i	$0.640928\pi$
$978$	1.30028e10	0.444478
$979$	−2.84166e10	−0.967905
$980$	−2.26955e9	−0.0770281
$981$	1.11908e10	0.378461
$982$	1.88988e10	0.636859
$983$	−1.18942e10	−0.399390	−0.199695	−	0.979858i	$-0.563995\pi$
$983$	−1.18942e10	−0.399390	−0.199695	+	0.979858i	$0.563995\pi$
$984$	−4.29599e9	−0.143741
$985$	5.17327e10	1.72480
$986$	2.58676e9	0.0859383
$987$	−5.33419e9	−0.176587
$988$	5.86541e8	0.0193486
$989$	7.29480e9	0.239787
$990$	−4.03472e9	−0.132157
$991$	1.37755e10	0.449623	0.224812	−	0.974402i	$-0.427823\pi$
$991$	1.37755e10	0.449623	0.224812	+	0.974402i	$0.427823\pi$
$992$	6.33556e9	0.206060
$993$	−1.64912e10	−0.534477
$994$	−1.03314e10	−0.333661
$995$	1.92871e10	0.620708
$996$	−5.44673e9	−0.174674
$997$	5.79135e10	1.85075	0.925373	−	0.379058i	$-0.123752\pi$
$997$	5.79135e10	1.85075	0.925373	+	0.379058i	$0.123752\pi$
$998$	−1.27936e10	−0.407415
$999$	2.54486e9	0.0807580

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.8.a.f.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.8.a.f.1.2	✓	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -301.420 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -301.420 q^{5} +216.000 q^{6} +343.000 q^{7} -512.000 q^{8} +729.000 q^{9} +2411.36 q^{10} -2295.22 q^{11} -1728.00 q^{12} -2197.00 q^{13} -2744.00 q^{14} +8138.34 q^{15} +4096.00 q^{16} -2505.49 q^{17} -5832.00 q^{18} -4171.46 q^{19} -19290.9 q^{20} -9261.00 q^{21} +18361.7 q^{22} +30284.2 q^{23} +13824.0 q^{24} +12729.0 q^{25} +17576.0 q^{26} -19683.0 q^{27} +21952.0 q^{28} +129054. q^{29} -65106.7 q^{30} -193346. q^{31} -32768.0 q^{32} +61970.9 q^{33} +20044.0 q^{34} -103387. q^{35} +46656.0 q^{36} -129293. q^{37} +33371.7 q^{38} +59319.0 q^{39} +154327. q^{40} -310763. q^{41} +74088.0 q^{42} +240878. q^{43} -146894. q^{44} -219735. q^{45} -242273. q^{46} +575985. q^{47} -110592. q^{48} +117649. q^{49} -101832. q^{50} +67648.4 q^{51} -140608. q^{52} +150363. q^{53} +157464. q^{54} +691824. q^{55} -175616. q^{56} +112630. q^{57} -1.03243e6 q^{58} +2.69804e6 q^{59} +520854. q^{60} -804145. q^{61} +1.54677e6 q^{62} +250047. q^{63} +262144. q^{64} +662220. q^{65} -495767. q^{66} -3.80152e6 q^{67} -160352. q^{68} -817673. q^{69} +827097. q^{70} +3.76508e6 q^{71} -373248. q^{72} +5.02926e6 q^{73} +1.03434e6 q^{74} -343684. q^{75} -266974. q^{76} -787259. q^{77} -474552. q^{78} -6.27040e6 q^{79} -1.23462e6 q^{80} +531441. q^{81} +2.48610e6 q^{82} +3.15204e6 q^{83} -592704. q^{84} +755206. q^{85} -1.92702e6 q^{86} -3.48447e6 q^{87} +1.17515e6 q^{88} +1.23808e7 q^{89} +1.75788e6 q^{90} -753571. q^{91} +1.93819e6 q^{92} +5.22034e6 q^{93} -4.60788e6 q^{94} +1.25736e6 q^{95} +884736. q^{96} +4.74801e6 q^{97} -941192. q^{98} -1.67321e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} - 108 q^{3} + 256 q^{4} - 134 q^{5} + 864 q^{6} + 1372 q^{7} - 2048 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q - 32 * q^2 - 108 * q^3 + 256 * q^4 - 134 * q^5 + 864 * q^6 + 1372 * q^7 - 2048 * q^8 + 2916 * q^9	\( 4 q - 32 q^{2} - 108 q^{3} + 256 q^{4} - 134 q^{5} + 864 q^{6} + 1372 q^{7} - 2048 q^{8} + 2916 q^{9} + 1072 q^{10} - 5443 q^{11} - 6912 q^{12} - 8788 q^{13} - 10976 q^{14} + 3618 q^{15} + 16384 q^{16} + 45437 q^{17} - 23328 q^{18} - 11194 q^{19} - 8576 q^{20} - 37044 q^{21} + 43544 q^{22} + 17762 q^{23} + 55296 q^{24} + 64926 q^{25} + 70304 q^{26} - 78732 q^{27} + 87808 q^{28} - 24980 q^{29} - 28944 q^{30} - 15419 q^{31} - 131072 q^{32} + 146961 q^{33} - 363496 q^{34} - 45962 q^{35} + 186624 q^{36} - 602081 q^{37} + 89552 q^{38} + 237276 q^{39} + 68608 q^{40} - 596814 q^{41} + 296352 q^{42} - 697726 q^{43} - 348352 q^{44} - 97686 q^{45} - 142096 q^{46} - 238097 q^{47} - 442368 q^{48} + 470596 q^{49} - 519408 q^{50} - 1226799 q^{51} - 562432 q^{52} + 752377 q^{53} + 629856 q^{54} - 2846467 q^{55} - 702464 q^{56} + 302238 q^{57} + 199840 q^{58} + 1651268 q^{59} + 231552 q^{60} + 178667 q^{61} + 123352 q^{62} + 1000188 q^{63} + 1048576 q^{64} + 294398 q^{65} - 1175688 q^{66} + 658872 q^{67} + 2907968 q^{68} - 479574 q^{69} + 367696 q^{70} + 191640 q^{71} - 1492992 q^{72} + 49572 q^{73} + 4816648 q^{74} - 1753002 q^{75} - 716416 q^{76} - 1866949 q^{77} - 1898208 q^{78} + 131485 q^{79} - 548864 q^{80} + 2125764 q^{81} + 4774512 q^{82} + 20201469 q^{83} - 2370816 q^{84} + 10179117 q^{85} + 5581808 q^{86} + 674460 q^{87} + 2786816 q^{88} + 13736753 q^{89} + 781488 q^{90} - 3014284 q^{91} + 1136768 q^{92} + 416313 q^{93} + 1904776 q^{94} + 21017342 q^{95} + 3538944 q^{96} + 572361 q^{97} - 3764768 q^{98} - 3967947 q^{99}+O(q^{100}) \) 4 * q - 32 * q^2 - 108 * q^3 + 256 * q^4 - 134 * q^5 + 864 * q^6 + 1372 * q^7 - 2048 * q^8 + 2916 * q^9 + 1072 * q^10 - 5443 * q^11 - 6912 * q^12 - 8788 * q^13 - 10976 * q^14 + 3618 * q^15 + 16384 * q^16 + 45437 * q^17 - 23328 * q^18 - 11194 * q^19 - 8576 * q^20 - 37044 * q^21 + 43544 * q^22 + 17762 * q^23 + 55296 * q^24 + 64926 * q^25 + 70304 * q^26 - 78732 * q^27 + 87808 * q^28 - 24980 * q^29 - 28944 * q^30 - 15419 * q^31 - 131072 * q^32 + 146961 * q^33 - 363496 * q^34 - 45962 * q^35 + 186624 * q^36 - 602081 * q^37 + 89552 * q^38 + 237276 * q^39 + 68608 * q^40 - 596814 * q^41 + 296352 * q^42 - 697726 * q^43 - 348352 * q^44 - 97686 * q^45 - 142096 * q^46 - 238097 * q^47 - 442368 * q^48 + 470596 * q^49 - 519408 * q^50 - 1226799 * q^51 - 562432 * q^52 + 752377 * q^53 + 629856 * q^54 - 2846467 * q^55 - 702464 * q^56 + 302238 * q^57 + 199840 * q^58 + 1651268 * q^59 + 231552 * q^60 + 178667 * q^61 + 123352 * q^62 + 1000188 * q^63 + 1048576 * q^64 + 294398 * q^65 - 1175688 * q^66 + 658872 * q^67 + 2907968 * q^68 - 479574 * q^69 + 367696 * q^70 + 191640 * q^71 - 1492992 * q^72 + 49572 * q^73 + 4816648 * q^74 - 1753002 * q^75 - 716416 * q^76 - 1866949 * q^77 - 1898208 * q^78 + 131485 * q^79 - 548864 * q^80 + 2125764 * q^81 + 4774512 * q^82 + 20201469 * q^83 - 2370816 * q^84 + 10179117 * q^85 + 5581808 * q^86 + 674460 * q^87 + 2786816 * q^88 + 13736753 * q^89 + 781488 * q^90 - 3014284 * q^91 + 1136768 * q^92 + 416313 * q^93 + 1904776 * q^94 + 21017342 * q^95 + 3538944 * q^96 + 572361 * q^97 - 3764768 * q^98 - 3967947 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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